Question 147045: Hi. I am writing is to inform you that I really need help in solving distance word problems. I also will ask you a specific question connected with age word problem. This has nothing to do with home work but I am planning on taking the graduate management admission test (GMAT) probably before the end of this year.
Here are the distance word problems, age word problem and questions connected to these problems:
Problem 1: A 555 mile, 5 hour plane trip was flown at two speeds. For the first part of the trip, the average speed was 105 mph. Then the tailwind picked up and the remainder of the trip was flown at an average speed of 115 mph. For how long did the plane fly at each speed?
Note: Do not worry about solving the word problem above. Just provide me with the response to the question below.
Here is the part of the equation that I have the question for you:
555-d=115(5-t).
Question 1: I want to know from the above equation, where does this minus "-" sign (555 "-"d=115(5-t) come from? I did read the above distance word problem and I did not see any key words connected with subtration (-). So I need to know where does the (-) come from?
Problem 2: A car and a bus set out at 2pm from the same point, headed in the same direction. The average speed of the car is 30 mph slower than twice the speed of the bus. In two hours the car is 20 miles ahead of the bus. Find the rate of the car.
Note: Do not worry about solving the word problem above. Just provide me with the response to the question below.
Here is part of the equation concerning problem 2.
d+20=2(2r-30).
Question 2: I want to know from the above equation, where does this plus "+" sign (d"+"20=2(2r-30) come from? I did read the above distance word problem and I did not see any key words connected with addition (+). So I need to know where does the (+) come from?
Age Word Problem
I noticed this equation with the solution from an age word problem:
H/2+1+H/3-1=20
H/2+H/3=20
3H+2H=120
5H=120
H=24
Question 3: I want to know from the above equation with the solution where does the 120 come from?
Here is the last question:
I solved this equation and I need to know if it is correct:
2r + 20 = 4r - 60
4r - 60
2r + 20
________
2r - 40
-- -- r = -20
2r 2r
The answer is -20. Am I correct?
Thank You.
Note: The above word problems come from a source other than a textbook. It is from a website (www.purplemath.com)
Answer by 24HoursTutor.com(40)   (Show Source):
You can put this solution on YOUR website! Problem 1
The simple formula below will help us solve the question :
distance = speed X time
The first average speed is = 105km/hr
Let us assume the duration the plane traveled at this speed to be x
The second average speed is =115km/hr
Let us assume the duration the plane traveled at this speed to be y
Now since we know that the total time taken was 5 hrs then the following must be also true :
x + y = 5
From this we can get :
y = 5 -x
Problem 2
Let us assume the speed of the bus to be x
The speed of the car is then = 2x - 30
Distance traveled = speed X time
So, distance traveled by car in 2 hours = 2(2x-30)
And distance traveled by bus = 2 X x = 2x
Now the distance traveled by car is 20 miles more so it means if we add 20 to the distance traveled by bus which is 2x then the distance traveled should be the same. So we can say :
2x+20 = 2(2x-30)
2x+20=4x-60
2x-4x=-60-20
-2x=-80
2x=80
x=80/2
x=40
x is the speed of the bus so now we can say that the speed of the bus is 40km/hr.
Speed of car = 2x-30
=2(40)-30
=80-30
=50
Answer: The average speed of the car is 50km/hr.
Now, distance traveled is 555 km and there are two different speeds at which the plane traveled.
The distance covered by traveling at 105km.hr = speed X time = 105x
The distance covered by traveling at 115km.hr = speed X time = 115y
Total Distance = 105x + 115 y
Now since we are already given the distance we get the following :
555 = 105x+115y
We have previously found out that y=5-x, so we can substitute it in the above equation to get :
555 = 105x + 115(5-x)
555 = 105x + 115x5 - 115x
555 = 105x - 115x + 575
555 = -10x + 575
555-575 = -10 x
-20 = -10x
10x = 20
x=20/10
x=2
Now y = 5-x =5-2 = 3
Ans.: The plane traveled at the speed of 105 km/hr for 2 hours(the value of x) and at the speed of 115km/hr for 3 hours(the value of y)
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